APR to APY Calculator
The same rate earns more when it compounds.
APR to APY Calculator
APY = (1 + APR / n)^n - 1, where n is the number of compounding periods per year.
Calculated instantly
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What This Calculator Does
The APR to APY Calculator converts a nominal annual percentage rate into the effective annual percentage yield for a chosen compounding frequency. It shows why two accounts advertising the same APR can pay different amounts over a year.
How It Works
The APR is divided by the number of compounding periods to get the periodic rate. One plus that rate is raised to the number of periods in a year, and one is subtracted to get the effective annual rate. Multiplying by 100 expresses it as a percentage. The balance field converts the rate difference into first-year interest and shows the simple-interest alternative for comparison.
Example
A 6 percent APR compounded monthly has a periodic rate of 0.5 percent. (1.005)^12 - 1 = 6.168 percent APY. On $10,000 that is about $616.78 of interest in the first year, compared with $600 at simple interest.
Formula
APR / compounding periods(1 + periodic rate)^periods - 1balance x APYAPY - APRReading the Results
Effective APY
The true annual growth rate if interest compounds at the chosen frequency and nothing is withdrawn.
First-year interest
APY applied to the balance you entered. It is a first-year illustration, not a projection of future rates.
APY minus APR
The compounding bonus in percentage points. It grows with the rate and the frequency, and is small at low rates.
Sources and References
Consumer Financial Protection Bureau - APR and APY explained
Annual percentage rate versus annual percentage yield
Explains how the two measures differ and why the compounding convention matters.
US SEC Investor.gov - Compound Interest
Compounding frequency and effective return
Investor-focused explanation of compounding and effective annual yield.
References identify the method or data behind this calculator. Where a standard or tariff changes, the current edition applies, and the assumptions stated above take precedence over a remembered figure.
Frequently Asked Questions
What is the difference between APR and APY?
APR is a nominal annual rate that ignores compounding within the year. APY, or effective annual rate, includes it. For savings, APY is the number to compare. For loans, APR may also include fees, so a loan APR is not directly comparable with a savings APY.
Why does more frequent compounding increase APY?
Interest is added to the balance more often, so later interest is earned on earlier interest. At 6 percent, annual compounding gives 6.000 percent, monthly gives 6.168 percent, and daily gives about 6.183 percent. The gain shrinks as frequency rises.
Can APY be lower than APR?
Not with positive nominal rates and more than one compounding period per year. APY equals APR when there is one annual compounding period and no fees. Negative rates or fee adjustments can change the relationship, but this calculator handles only the nominal rate.
Does this include account fees?
No. It converts a nominal rate, not a full APR disclosure. A loan APR includes certain finance charges, and a savings account may have maintenance fees that reduce the effective return. Read the account terms and the loan estimate.
How do I use this for a loan?
Use it to see the effect of compounding on a nominal rate, but do not treat the result as the loan APR. Loan APR includes fees and is calculated under specific disclosure rules. For borrowing, compare the APR on the loan estimate and the total interest over the term.